JEE Mains · Maths · STD 12 - 6. Application of derivatives
the tangent at the point \(\left(x_{1}, y_{1}\right)\) on the curve \(y=x^{3}+3 x^{2}+5\) passes through the origin, then \(\left(x_{1}, y_{1}\right)\) does NOT lie on the curve
- A \(x^{2}+\frac{y^{2}}{81}=2\)
- B \(\frac{ y ^{2}}{9}- x ^{2}=8\)
- C \(y=4 x^{2}+5\)
- D \(\frac{x}{3}-y^{2}=2\)
Answer & Solution
Correct Answer
(D) \(\frac{x}{3}-y^{2}=2\)
Step-by-step Solution
Detailed explanation
The tangent at \(\left(x_{1}, y_{1}\right)\) to the curve \(y=x^{3}+3 x^{2}+5\) \(y-y_{1}=\left(3 x_{1}^{2}+6 x_{1}\right)\left(x-x_{1}\right) \text { passing through origin }\) \(-y_{1}=\left(3 x_{1}^{3}+6 x_{1}\right)\left(-x_{1}\right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The area of the region given by \(\left\{(x, y): x y \leq 8,1, \leq y \leq x^2\right\}\) is :JEE Mains 2023 Hard
- The sum of all local minimum values of the function is
\(
f(x)=\left\{\begin{array}{lr}
1-2 x, & x \lt -1 \\
\frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\
\frac{11}{18}(x-4)(x-5), & x\gt2
\end{array}\right.
\)JEE Mains 2025 Medium - Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum of \((n+1)\) terms \({ }^{n} C_{0}, 3 .{ }^{n} C_{1}, 5 .{ }^{n} C_{2}, 7 .{ }^{n} C_{3}, \ldots\) is equal to \(2^{100} \cdot 101\), then \(2\left[\frac{n-1}{2}\right]\) is equal to \(....\)JEE Mains 2021 Hard
- Let \(y=y(x)\) be the solution of the differential equations \(\frac{d y}{d x}+\frac{5}{x\left(x^5+1\right)} y=\frac{\left(x^5+1\right)^2}{x^7}, x > 0\). If \(y(1)=2\), then \(y(2)\) is equal toJEE Mains 2023 Hard
- Let the equations of two adjacent sides of a parallelogram \(A B C D\) be \(2 x-3 y=-23\) and \(5 x+4 y\) \(=23\). If the equation of its one diagonal \(AC\) is \(3 x +\) \(7 y=23\) and the distance of A from the other diagonal is \(d\), then \(50 d ^2\) is equal to \(........\).JEE Mains 2023 Hard
- The number of distinct real roots of \(x ^{4}-4 x +1=0\) isJEE Mains 2022 Medium
More PYQs from JEE Mains
- If the local maximum value of the function \(f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, \quad x \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{k}{e}\), then \(\left(\frac{ k }{ e }\right)^8+\frac{ k ^8}{ e ^5}+ k ^8\) is equal toJEE Mains 2023 Hard
- For all complex numbers \(z\) of the form \(1 + i\alpha\), \(\alpha \in R\) , if \(z^2\, = x + iy\), thenJEE Mains 2014 Hard
- Let \(\alpha>0, \beta>0\) be such that \(\alpha^{3}+\beta^{2}=4 .\) If the maximum value of the term independent of \(x\) in the binomial expansion of \(\left(\alpha x^{\frac{1}{9}}+\beta x^{-\frac{1}{6}}\right)^{10}\) is \(10 k\) then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- The number of the real solutions of the equation : \( x|x+3|+|x-1|-2=0 \) isJEE Mains 2026 Easy
- Let \(f(x)=2 x+\tan ^{-1} x\) and \(g(x)=\log _e\left(\sqrt{1+x^2}+x\right)\), \(x \in[0,3]\). ThenJEE Mains 2023 Hard
- If \(S\) is the sum of the first \(10\) terms of the series \(\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots\) then \(\tan ( S )\) is equal toJEE Mains 2020 Medium